Category:Polyominoes

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A polyomino is a polyform with the square as its base form. It is a connected shape formed as the union of one or more identical squares in distinct locations on the plane, taken from the regular square tiling, such that every square can be connected to every other square through a sequence of shared edges (i.e., shapes connected only through shared corners of squares are not permitted).

n	Subcategory	Number of free polyominoes	Number of free polyominoes with holes	Number of one-sided polyominoes	An = number of fixed polyominoes
1	Monominoes	1	0	1	1
2	Dominoes	1	0	1	2
3	Trominoes	2	0	2	6
4	Tetrominoes	5	0	7	19
5	Pentominoes	12	0	18	63
6	Hexominoes	35	0	60	216
7	Heptominoes	108	1	196	760
8	Octominoes	369	6	704	2,725
9	Nonominoes	1,285	37	2,500	9,910
10	Decominoes	4,655	195	9,189	36,446
11	Undecominoes	17,073	979	33,896	135,268
12	Dodecominoes	63,600	4,663	126,759	505,861